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DOI 10.1007/s10888-015-9301-7Alternative weighting structures for multidimensional
poverty assessment
Danilo Cavapozzi· Wei Han · Raffaele Miniaci
Received: 15 January 2014 / Accepted: 18 February 2015 © Springer Science+Business Media New York 2015
Abstract A multidimensional poverty assessment requires a weighting scheme to aggre-gate the well-being dimensions considered. We use Alkire and Foster’s J. Public Econ. 95, 476–487 (2011a) framework to discuss the channels through which a change of the weight-ing structure affects the outcomes of the analysis in terms of overall poverty assessment, its dimensional and subgroup decomposability and policy evaluation. We exploit the Survey on Health, Ageing and Retirement in Europe to evaluate how alternative weighting structures affect the measurement of poverty for the population of over-50s in ten European coun-tries. Further, we show that in our empirical exercise the results based on hedonic weights estimated on the basis of life satisfaction self-assessments are robust to the presence of heterogeneous response styles across respondents.
Keywords Anchoring vignettes· Life satisfaction · Multidimensional poverty measurement· Weighting schemes
D. Cavapozzi ()
Department of Economics, Ca’ Foscari University of Venice, Fondamenta San Giobbe, Cannaregio 873, 30121 Venezia, Italy
e-mail: danilo.cavapozzi@unive.it D. Cavapozzi
Netspar, Tilburg, The Netherlands W. Han
Blavatnik School of Government, University of Oxford, Albion House, Littlegate Street, OX1 1AN, Oxford, UK
e-mail: wei.han@bsg.ox.ac.uk R. Miniaci
Department of Economics and Management, University of Brescia, Via S.Faustino 74/b, 25122 Brescia, Italy
e-mail: raffaele.miniaci@unibs.it R. Miniaci
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1 IntroductionDuring the past decades it has been gradually recognized that the concept of well-being cannot be comprehensively captured by any conventional unidimensional indicator based on income, consumption or expenditure (Nussbaum2001; Sen1985). Focusing on a unique dimension keeps blind of the information about the overall life quality, of which it might be worthwhile for policy-makers to keep track given that pursuing well-being rather than wealth itself appears to be the ultimate goal of human society (Ruger2010).
Although the multidimensional perspective on well-being measurement moves beyond the focus on a single indicator, it is still far from reaching an agreement on how to translate this perspective into practice. One of the complex and highly debatable issues emerging in a multidimensional context of well-being research lies in how to set the relative weights across the dimensions. Summarizing the achievements with respect to different well-being dimensions in a single indicator is needed to measure the diffusion of poverty, defined as pronounced deprivation in well-being, within a population.
This paper is aimed at showing how the adoption of different weighting schemes affects the outcomes of a multidimensional poverty study. We choose to conduct our analysis based on the Alkire and Foster’s multidimensional poverty framework (Alkire and Foster2011a). One of its advantages lies in that it allows exploiting the information coming from achieve-ments measured on ordinal and categorical scales, which is of significant importance in the policy analysis. Despite the fact that this approach is not the only one that can deal with ordinal or categorical variables,1 it is the one most used in informing policy. The United Nations Development Programme has been including the Multidimensional Poverty Index (MPI) inspired by the Alkire and Foster’s method in the Human Development Report since 2010. Besides, a Multidimensional Poverty Peer Network including Ministers and senior officials from 22 countries and 5 institutions has been established recently to promote the application of MPI in policy making.
According to the Alkire and Foster’s approach, well-being dimensions are described by a set of one or more achievement indicators. The results with respect to the whole battery of achievement indicators can be aggregated into a single well-being score according to a weighting structure specified a priori. Poor households are those whose well-being scores fail to reach a minimum threshold. Alkire and Foster (2011a) propose a poverty measure, the adjusted headcount ratio, which reflects prevalence of poverty in the population and the intensity of the poverty among the poor. This measure can be decomposed in order to assess both the contribution of each dimension to overall poverty and how poverty varies across subgroups. The subgroup decomposability of the adjusted headcount ratio is also useful to investigate the determinants of the variations in poverty measurement originated by changes in the weighting scheme or in the distribution of the achievements in the population. In both cases it is possible to recognize a first part of the variation due to the change in the pool of families identified as poor and a second part due to the change in well-being of those families who are identified as poor regardless of the weighting scheme adopted or the distribution of achievements considered. The decomposition allows the researcher to investigate if the poverty assessment changes mainly because the set of households in poverty varies or because of variations in the well-being of the poor households.
1See Aaberge and Peluso (2012), Bosmans et al. (2013), Bossert et al. (2013), and Decancq et al. (2014) and
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Various approaches to the choice of the weighting schemes have been proposed in the literature. Decancq and Lugo (2013) surveyed three main classes of weights: normative, data-driven and hybrid. Normative weights are based on an explicit value judgment of ana-lysts about the trade-offs between the well-being dimensions. Data-driven weights are based on the actual distribution of the achievements in the society with respect to the indicators of interest. Hybrid weights combine value judgements and statistical facts. They lie in the mid-dle between defining weights by arbitrary decisions of analysts and letting data distribution be the only criterion used.How poverty assessments are affected by the weighting scheme remains an empirical issue. In our exercise, we focus on the elderly population in Europe, follow the classifica-tion by Decancq and Lugo (2013) and choose one example for each of the classes discussed above. As for normative weights, we use equal weighting, which is the weighting scheme most widely used in measuring multidimensional well-being due to its simplicity.2We fol-low the Human Development Index and MPI to assign equal weights to each dimension and equal weights to each achievement indicator in each dimension (UNDP2011).3Within the class of data-driven weights, we adopt the frequency weights, which are motivated by the idea that, when assessing well-being, individuals put a high value on the shortfalls where the majorities do not fall short. We follow Desai and Shah (1988) to set the weight of a given achievement indicator as the corresponding proportion of the non-deprived in the society. Finally, within the hybrid class, we choose the hedonic weights, that is weights derived from life satisfaction self-assessments. Doing so we circumvent one of the weak-nesses of the equal weighting, that is, that the value judgement about dimension trade-offs is set a priori by researchers. In fact, as noticed by Kingdon and Knight (2006, p. 1204) “[t]he value judgement implicit in this weighting need not correspond at all well to the val-uations of these capabilities made by individuals in society. Subjective well-being may be a narrow metric but at least it corresponds to individual valuations and it is a metric that can be measured.” A possible drawback of hedonic and frequency weights is that they are time-and population-specific: as the distribution of achievements time-and preferences can vary across households and over time, the use of the same set of these weights for various subgroups or time periods needs extra caution with respect to the adoption of the normative weights.
Many social science surveys ask respondents to rate their satisfaction with life accord-ing to a predetermined scale usually spannaccord-ing from “very dissatisfied” to “very satisfied”. Life satisfaction self-assessments have been widely used in the applied research focus-ing on well-befocus-ing determinants (see for instance Frey and Stutzer2002, and Dolan et al.
2008). When dealing with self-reported life satisfaction data it is important to recognize that, as a subjective measure, its variability across socioeconomic groups can be ascribed to genuine differentials in well-being (Schokkaert 2007) as well as heterogeneity in the way in which individuals with different characteristics interpret the scale used to provide self-assessments. As an example, two individuals might have different expectations about the conditions that should realize to self-define as satisfied with their lives. Then, even if they experience the same level of well-being, they might produce different self-assessments due to their different reporting styles. Neglecting such heterogeneity when studying life satisfaction determinants might end up with assigning to an explanatory variable a biased role coming from the combination between its relationship with the reporting style used
2It has been employed in approximately 50 % of the published studies (see Decancq and Lugo2013). 3It can be set equally either at the dimension level or at the indicator level. Inherently, it is an arbitrary
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in life-satisfaction self-assessments and its actual role in explaining genuine differences in well-being (see King et al.2004, and Angelini et al.2012,2014).Fleurbaey et al. (2009) and Decancq et al. (2014) suggest a framework for poverty mea-surement that explicitly takes into account individual preferences. They elicit the relative concerns of the individuals about the various dimensions of well-being based on life sat-isfaction self-assessment regressions. They exploit the longitudinal nature of their data to control for the possible role played by heterogeneity in response styles. In a similar spirit, we use the estimated coefficients of a statistical model that relates the stated life satisfaction levels with the achievement indicators to derive the weights of the latters in the well-being score function of Alkire and Foster (2011a). As in Fleurbaey et al. (2009) and Decancq et al. (2014), we also take into consideration the presence of response style heterogeneity, but we tackle this problem in a different way.
To this end, we exploit the information made available by the Survey of Health, Age-ing and Retirement in Europe (SHARE). SHARE is a cross-country study that administers a multi-disciplinary questionnaire to a representative sample of individuals aged 50 or more living in Europe. Moreover, the second wave of SHARE provides us with a survey-instrument designed to take into account heterogeneity in the reporting styles used in collecting subjective data on life satisfaction. This approach is based on anchoring vignettes. A representative subsample of respondents is asked to report their own life satisfaction self-assessments along with their assessments about the life satisfaction of hypothetical individuals described in vignettes kept constant across respondents. Differences in vignette-evaluations provided by respondents can then be of use to identify heterogeneity in reporting styles and disentangle such variability from actual differentials in well-being. We therefore estimate two sets of hedonic weights, the first based on the estimates of the relation-ship between life satisfaction self-assessments, achievement indicators and individuals’ characteristics, the second that formally controls also for the heterogeneity in reporting styles.
We therefore investigate the multidimensional poverty of the elderly in Europe using four sets of weights to ascertain to what extent the weighting scheme adopted affects poverty assessment and to shed light on the robustness of the results based on hedonic weights with respect to the relaxation of the assumption of invariance of reporting styles in the population. The paper is organised as follows. Section2describes Alkire and Foster’s multidimen-sional poverty framework that our analysis is built on. Section3is devoted to describe the approach we follow to derive the hedonic weights used in our analysis. Section4describes the data used in our empirical exercise and all the ingredients, but weights, involved in our application of the Alkire and Foster’s multidimensional framework. Results are reported in Section5. Section6presents our conclusions and policy implications.
2 A framework for the multidimensional poverty assessment
Sen (1976) concisely summarized two problems that must be faced in the poverty measure-ment: (1) the identification problem, i.e. how to choose the criterion of poverty and then distinguish those who fall into that criterion and those who do not; and (2) the aggregation problem, i.e. how to construct a poverty index using the available information on the poor. Dealing with these two issues is particularly challenging in a multidimensional framework. Alkire and Foster (2011a) tackle the identification problem by defining indicator-specific thresholds – which refer to specific achievements – and an overall threshold, which refers to a comprehensive well-being score based on the achievements. Moreover, they adopt the
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Foster et al. (1984) framework to handle the aggregation problem and deliver a methodology satisfying desirable properties for poverty measurement.In our brief introduction to Alkire and Foster’s method, for sake of simplicity and without loss of generality, we assume that each dimension is represented by one indicator. All the results can be easily generalized to the case in which more indicators are considered for each dimension.
The units of our analysis are n households. Each dimension, k = 1, 2 . . . D is described by the achievement of household h on the k-th dimension, ykh. Every dimension has its own threshold, zk, to indicate the minimum standard to attain to be not deprived. Let wkbe the
weight of the k-th dimension, the weights sum up to 1, i.e.
D
k=1
wk = 1. The first step of
Alkire and Foster’s identification procedure defines the achievement status of household h in terms of the dimension k as ahk = μykh> zk, where μ(·) = 1 if the expression in
parentheses is true, zero otherwise. The problem of aggregation across dimensions is solved by defining a scalar well-being function as weighted average of dimension achievement statuses, that is by computing the overall well-being score of household h:
sh=
D
k=1
akhwk (1)
Finally, Alkire and Foster’s procedure identifies as poor those households whose well-being score is lower than an arbitrarily chosen well-well-being threshold ϕ, with ϕ (0,1). More formally, the poverty status of household h is defined as Ph= μsh< ϕ.
The standard method to overcome the aggregation problem is to refer to the poverty incidence measured by the headcount ratio:
H = 1 n n h=1 Ph (2)
However, this index violates the dimensional monotonicity property, that is, other things being constant, if the shortfall of those identified as ‘poor’ varies, the headcount index remains unchanged.4 As early as in Sen’s well-known paper on the ordinal approach to poverty measurement (Sen1976), monotonicity has been listed as one of the most important axioms that a valid poverty index should satisfy. The adjusted headcount ratio M, proposed by Alkire and Foster (2011a), satisfies the monotonicity axiom by combining information on the incidence of the poor in the population with the degree of poverty among the poor. The former is measured by the headcount ratio H ; the latter is measured by the average shortfall among the poor:
A= n h=1Ph 1− sh n h=1Ph (3) Formally, the adjusted headcount ratio is
M= HA = 1 n n h=1 Ph1− sh (4)
4In this paper, shortfall refers to the gap between the actual well-being score s
hand the full well-being score
(i.e. when all the minimum standards are met and sh= 1) rather than to the gap with respect to the well-being threshold ϕ.
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which also represents the total shortfall experienced by the poorn
h=1
Ph1− sh divided by the maximum shortfall that could be experienced by the entire population. When none of the households meet any minimum standard with respect to any indicator, sh =
D
k=1akhwk= 0 and thushn=1Ph1− sh= n.
The adjusted headcount ratio satisfies a range of desirable properties for poverty indexes5(see Alkire and Foster2011a). In particular, the decomposability by subgroup and dimension is of significant importance to policy makers.
Subgroup decomposability The adjusted headcount ratio M in the population is the weighted average of the same measure calculated for mutually exclusive subgroups, where weights are subgroup population shares. Formally, suppose population can be divided into qgroups. Let θgbe the population share of subgroup g. Denote the adjusted headcount ratio
of subgroup g as Mg, so we have M = q
g=1θgMg
. The relative contribution of subgroup g to overall poverty M depends on both θgand Mgand can be written as RGg= θgMMg.
Dimensional decomposability The overall poverty measure M is the weighted average of the censored deprivation indexes of each dimension, where the weights are the dimension-specific weights. The censored deprivation index Ik for the dimension k is the fraction of
households who are poor and deprived with respect to the k-th dimension: Ik= 1 n n h=1 Ph[(1 − a]hk) (5) The term “censored” is used to emphasize that Ik considers only the deprivation status
of the poor. The overall adjusted headcount ratio can be written as M=
D
k=1
Ikwk, (6)
and the relative contribution of the dimension k to the overall poverty is RDk = IkMwk. If
more than one indicator is used to describe a dimension, the relative contribution of the dimensions is the summation of the relative contributions of the indicators in that dimension.
The definition of the well-being score, sh = D
k=1akhwk, makes apparent that
chang-ing the weights potentially has influence on who is identified as poor, on the headcount and the adjusted headcount ratios and on the dimensional as well as subgroup decompositions. The overall effects on the poverty assessment are difficult to predict. This is not a peculiar-ity of the Alkire and Foster’s approach. It is true for any index that aggregates individual positions and/or various dimensions, because of the role played by the joint distribution of the dimensions in the population (see e.g. Paruolo et al.2013). Comparing alternative poverty assessments produced by alternative weighting schemes is standard practice in the literature (e.g. Bourguignon and Chakravarty2003). We also run a similar exercise in the empirical section of the paper, but we enrich this practice by suggesting a decomposition
5It satisfies the following properties: replication invariance, symmetry, poverty and deprivation focus, weak
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of the variation of the adjusted headcount index that provides insights on the mechanisms originating it.More specifically and without loss of generality, consider the simple case of two weight-ing schemes w and w, that differ for the weights of the indicators p and q, with wp−wp=
wq−wq.6The two sets of weights generate potentially different well-being scores for every
household and consequently different pools of families identified as poor. We define nout
as the number of households identified as poor with the weighting scheme w but out of poverty with the new score vector w, ninis the number of households falling in poverty
with the weighting scheme w(but not with w), and finally nstayare the households who are
identified as poor under both weighting schemes. Using the group decomposition property of the adjusted headcount ratio, the overall variation M = M− M can be written as the weighted average of the variations of the ratios of the three groups of households mentioned above: M= nout n Mout+ nin n Min+ nstay n Mstay (7)
where the in, out and stay subscripts identify the pools of households the ratios Mand M refer to. The adjusted headcount ratio equals zero whenever it is computed over a set of non-poor households, then Mout = Mout − Mout = −Mout, Min= Min − Min = Min ,
and the expression above can be rewritten as M=nin n M in− nout n Mout +nstay n Mstay= M1+ M2 (8) The M1term reflects a composition effect driven by the households who change their poverty status from one weighting scheme to the other. The term M2is instead driven by the effect of the change in the weighting scheme on the well-being score of the households who are poor regardless of the weighting scheme used. Consequently, it is impossible to predict the sign of M without knowing the underlying distribution of all the indicators within the sets of households changing their poverty status or remaining poor under both weighting schemes.
The group decomposability of the adjusted headcount ratio is also useful to analyse situations in which the weights remain constant, but the distribution of the achievements in the population changes. Consider for instance the case in which the adjusted head-count ratio is used to evaluate the effectiveness of an anti-poverty policy that targets the households deprived in the dimension p. Only the households who did not meet the minimum standard of indicator p and were identified as poor before the intervention con-tribute to reduce the original level of the adjusted headcount ratio M. Define M the poverty measure after the intervention, the variation of interest M = M− M can be decomposed as:
M= nout
n Mout+ nstay
n Mstay (9)
where the out subscript identifies the pools of households beneficiary of the policy that exit the poverty status thanks to the intervention, while stay identifies the beneficiaries who do not change their poverty status. It can be shown that for the first group of households
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Mout = −Mout, while for the latter is Mstay= −wp. The decomposition can thereforebe written as M = −nout n Mout+ nstay n wp = M1+ M2. (10) The expression above makes apparent that the effect of the policy is larger the larger the number of households escaping poverty (nout), the more deprived are these households
(Mout)and the higher is the weight associated with the targeted dimension (wp). Changing
the weighting scheme changes not only the overall effect M but also the relative impor-tance of M1and M2. The latter effect impacts on the assessment of the relevance of the mechanisms that make the policy intervention effective.
3 Deriving weights with the hedonic approach
The hedonic approach of deriving a weighting scheme is hybrid since it combines value judgements about trade-offs among dimensions, as it is typical in the normative weighting, with statistical facts. We use life satisfaction self-assessments of respondents to elicit value judgements about trade-offs between well-being dimensions. A widely used approach to measure well-being in applied research is to ask individuals to evaluate their life satisfaction according to a predetermined scale, e.g. by answering the question “How satisfied are you with your life in general?”. Self-assessments are measured according to an ordinal scale, such as “Very dissatisfied”, “Dissatisfied”, “Neither satisfied nor dissatisfied”, “Satisfied”, “Very satisfied”. Frey and Stutzer (2002) and Dolan et al. (2008) survey the main findings of the empirical research on the determinants of life satisfaction self-assessments.
On the one hand, life satisfaction self-assessments have the advantage of summarizing in a single index all the factors that individuals consider relevant determinants of their well-being. On the other hand, a recent research vein (Angelini et al.2012and2014, Kapteyn et al.2009) has shown that the benchmarks used to self-evaluate life satisfaction are not invariant across individuals but depend on their own characteristics. Even if individuals are asked to self-evaluate their own life satisfaction according to the same survey question, they might provide different evaluations due to inter-personal and inter-cultural heterogeneity in the interpretation of the response scale. Furthermore, a phenomenon of adaptation might be at work. In fact, individuals may adjust their aspiration levels to their realistic opportunities (Schokkaert2007). In psychometrics such heterogeneity has been called differential item functioning (DIF). If DIF is an issue, life satisfaction self-assessments fail to be comparable across individuals or socioeconomic groups since their differences might not reflect actual differences in well-being but only differences in the reporting styles adopted by respondents. Individuals with the same actual level of well-being might provide different life satisfaction self-evaluations because they have in mind different concepts about what being satisfied with their life means. As a consequence, the presence of DIF implies that a well-being anal-ysis based on the comparison of life satisfaction self-evaluations should take into account heterogeneity in reporting styles in order to provide meaningful results.
This paper takes advantage of the SHARE data to control for DIF by a vignette method-ology. After having provided life satisfaction self-assessments, a subsample of SHARE respondents are asked to evaluate the life satisfaction of two hypothetical individuals described in particular situations (anchoring vignettes), which are reported below.
1. John is 63 years old. His wife died 2 years ago and he still spends a lot of time thinking about her. He has 4 children and 10 grandchildren who visit him regularly. John can
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make ends meet but has no money for extras such as expensive gifts to his grandchil-dren. He has had to stop working recently due to heart problems. He gets tired easily. Otherwise, he has no serious health conditions. How satisfied with his life do you think John is?2. Carry is 72 years old and a widow. Her total after tax income is about C1,100 per month.7 She owns the house she lives in and has a large circle of friends. She plays bridge twice a week and goes on vacation regularly with some friends. Lately she has been suffering from arthritis, which makes working in the house and garden painful. How satisfied with her life do you think Carry is?
Respondents’ evaluations of vignettes are recorded according to the same response scale used for their self-assessments (“Very dissatisfied”, “Dissatisfied”, “Neither satisfied nor dissatisfied”, “Satisfied”, “Very satisfied”).
The situations described in the vignettes do not vary across respondents, who are also explicitly asked to evaluate the vignettes according to their own preferences. Differ-ences in the evaluations of the anchoring vignettes can be ascribed to the heterogeneity in the reporting styles of respondents and be of use to filter the life satisfaction self-assessments of respondents from DIF as long as respondents use the same reporting style when assessing the life satisfaction of themselves and of the hypothetical individuals described in the vignettes (response consistency) and the life satisfaction of the hypothet-ical individuals in the vignettes is on average perceived by respondents in the same way (vignette equivalence).
More specifically, we analyze the determinants of life satisfaction and control for the presence of DIF by the hierarchical ordered probit (Hopit) model introduced by King et al. (2004). This econometric specification consists of two components modeling self-assessments and vignette evaluations as ordered variables.
Self-assessment component Let Yi∗ be the life satisfaction perceived by individual i = 1, . . . , I and assume that it comes from a linear combination of individual charac-teristics stored in the row vector Xi and an error term εi ∼ N(0, 1) independent
of Xi,
Yi∗= Xiβ+ εi (11)
where β is a vector of unknown parameters. The vector Xiincludes the achievement
indica-tors as well as the individual characteristics related to their frame of reference (see Fleurbaey et al. 2009). Controlling for the individual characteristics is also “necessary to ‘clean’ the happiness measure to separate the ‘ethically’ relevant information from the irrelevant noise” (Schokkaert2007, p. 428). Although Yi∗cannot be observed, we know individual’s life satisfaction self-evaluation Yi, which is coded as an ordered discrete variable
span-ning from 1 (“Very dissatisfied”) to 5 (“Very satisfied”). The transformation connecting the unobserved continuous variable Yi∗with the observed discrete outcome Yi can be written
as follows
Yi= j if τij−1≤ Yi∗≤ τji j = 1, . . . , 5 (12)
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The thresholds τijare individual-specific and depend on Xiτi0 = −∞, τi5= ∞ (13) τi1 = Xiγ1 (14) τij = τij−1+ exp Xiγj , j= 2, 3, 4 (15) where γjare vectors of unknown parameters. Notice that X
iγj, j = 2, 3, 4 is the argument
of the exponential function to ensure the ascending order of the thresholds. The set of thresh-olds τijand the parameters γj formally allow individuals with different characteristics and achievements to provide different self-evaluations Y despite the same perceived level of life satisfaction Y∗. The Hopit model can then be seen as a generalization of the standard ordered probit specification, which restricts the thresholds to be invariant across individuals and implicitly assumes that reporting styles adopted by individuals do not depend on their own characteristics.
The self-assessment component of the Hopit model formally shows that the effect of Xi
on the observed outcome Yi is twofold since Xi affects the life satisfaction perceived by
individuals Yi∗as well as the way in which such perception is reported on a discrete scale, which is summarized by the thresholds τij. The information conveyed by life satisfaction self-evaluations is not sufficient to disentangle the effect of the individual characteristics Xi
on Yi∗and their effect on the thresholds τij. We make use of vignette evaluations to achieve this goal and identify the parameter vectors β and γj.
Vignette evaluation component Let Zil∗be the life satisfaction of the hypothetical person in vignette l= 1, 2 perceived by individual i. We assume that
Z∗il= θl+ vil (16)
where vil ∼ N0, σl2and vil is independent of εi and Xi. The parameter θlis assumed
to be vignette-specific and invariant across individuals. This restriction follows from the vignette equivalence assumption, according to which respondents have the same perception of the life satisfaction of the hypothetical person in the vignette up to an individual idiosyn-cratic error term. Again, we cannot observe the perception Z∗ilbut we know the evaluation Zil, defined as
Zil= j if τij−1≤ Z∗il≤ τ j
i, j = 1, . . . , 5 (17)
The response consistency assumption implies that thresholds τij are those used to derive the life satisfaction self-assessments and therefore we can combine the information relevant for the two components of the model to identify all the parameters of interest in the Hopit model. Along the lines of King et al. (2004), the joint estimation can be carried out by maximum likelihood techniques.
We estimate two sets of hedonic weights. The first one derived from a standard ordered probit regression. The standardized weight for the achievement indicator k, wk, is retrieved
from the corresponding estimated coefficients ˆβkas
wk=
ˆβk
D l=1 ˆβl
k= 1, . . . , D (18) The second set of standardized hedonic weights is derived from the estimated coeffi-cients of the achievement indicators in the self-assessment component of the Hopit model.
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This vector of hedonic weights is expected to reflect the relationship between achieve-ment indicators and well-being once their effect on reporting styles in life satisfaction self-assessments has been filtered out.4 Data, dimensions, indicators and thresholds
In this paper we use data from the 2006 wave of the Survey of Health, Ageing and Retire-ment in Europe (SHARE). SHARE is an interdisciplinary survey on ageing that is run every two years and collects extensive information on health, socioeconomic status and family interactions of individuals aged 50 and over in a host of European countries.8The choice of using SHARE rather than other well established surveys (e.g. EU-SILC for the Euro-pean countries) is dictated by the fact that SHARE collects self-assessments and anchoring vignette evaluations on life satisfaction and makes it possible to investigate if the hedo-nic weights based on the life satisfaction self-assessments of respondents are robust to the presence of heterogeneity in response styles.
Data are collected by face-to-face, computer-aided personal interviews (CAPI), sup-plemented by a completion paper and pencil questionnaire, which collects self-assessments and vignette evaluations on life satisfaction. We select only those respondents who provide both the self-evaluation and at least one vignette evaluation. Our final estima-tion sample for the hedonic weights is composed by 3,804 households, corresponding to 5,545 individuals living in Sweden, Denmark, Germany, The Netherlands, Belgium, France, Greece, Italy, Spain and Czech Republic.9
Different multidimensional poverty indexes consider alternative sets of dimensions due to differences in theoretical perspectives, reference population and data limitation. Accord-ing to Sen (2004), the choice of the dimensions should focus: (1) on those that are of special importance to the society or people in question; (2) on those that are an appropriate focus for public policy, rather than a private good or a capability that cannot be influenced from outside. Material deprivation, health conditions, educational attainments, empowerment, labour market participation, environmental quality, safety from violence, and social rela-tionships are all relevant domains and their relevance has been assessed for the European Union population (Eurostat2012).
In our illustrative exercise we focus on a representative sample of elderly respondents living in ten European countries and we consider three dimensions to represent the main drivers of their well-being: economic situation, housing and health conditions. The eco-nomic dimension is meant to describe the monetary resources available to the household. It includes two achievement indicators: per-capita net income and per-capita net wealth. The thresholds for income and wealth indicators are set equal to 60 % of the country specific median values. By doing so, we follow Stiglitz’s Commission suggestions to con-sider both income and wealth. The housing dimension has one achievement indicator, a measure of accessibility of the dwelling given by the number of steps people have to climb up and/or down to the entrance of their home. The architectural barriers of the accommodation are potentially relevant for the population we consider, as ageing is often
8See B¨orsch-Supan et al. (2008) for further details.
9We restrict our sample to the countries in which vignette data have been collected with the exception of
Poland, for which the data used for the analysis show some inconsistency with respect to the rest of the sample.
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accompanied by limitation to the mobility. In our sample, 44 % of respondents report lim-itations with mobility, arm functions and fine motor function. This percentage is greater than 50 % for Belgium, Czech Republic, Greece and Italy. We considered also some over-crowding indicators, but, once controlled for other dimensions, none of them proved to have any significant effect on the self-assessed life satisfaction of the households. Unfor-tunately, we do not have information on the quality of the neighbourhood for most of the estimation sample.Finally, we use three achievement indicators for the health domain: the presence of chronic diseases (in a list of 17 diseases) and the number of limitations with the activi-ties of daily living (ADL, that is dressing, walking across a room, bathing or showering, eating, getting in and out of bed, using the toilet) to take into consideration physical health, and the presence of depression symptoms (EURO-D caseness, see Prince et al.
1999) to summarize mental wellbeing. The inclusion of an indicator of depression symp-toms may be controversial because it could make more difficult the elicitation of the preferences and the estimation of the hedonic weights from questions on life satisfac-tion. In fact, the respondents may not clearly distinguish between the cognitive valuation of their life and their depressed feelings (see Fleurbaey et al.2009). We decided to con-sider EURO-D caseness because mental wellbeing is a crucial dimension of the overall individual well-being and public intervention in this field has been often advocated (e.g. Nussbaum2008). Moreover, the Hopit model takes explicitly into consideration that the depressed feelings may alter individuals’ response styles, and by doing so it improves the possibility to separately identify the cognitive component of the life satisfaction evaluation.
Table1 summarizes the details about the dimensions, the achievement indicators and the corresponding thresholds used to define the presence of deprivation.10 Rephrasing Alkire and Foster’s (2011b) words, the aim of our empirical exercise is not to suggest that this set of indicators, dimensions and cut-offs is appropriate in every application. Rather, the aim of our illustrative exercise is twofold. On the one hand, we aim at describing the effects of changes in weighting schemes on the outcomes of the multidi-mensional poverty analysis run according to the Alkire and Foster’s methodology on a sample of elderly individuals living in ten European countries. On the other hand, we want to assess the robustness of the results obtained with hedonic weights based on respon-dents’ life satisfaction self-assessments with respect to the presence of heterogeneity in reporting styles.
The proportion of households who meet the minimum standards with respect to sin-gle indicators ranges between 44.5 % for the presence of chronic diseases to 86.3 % for the presence of impediments with the activities of daily living. It is important to notice that the indicators are only weakly correlated between them (Table 2). This suggests that the information conveyed by the indicators considered is not statistically redundant.
Unlike the thresholds of the indicators (zk) that can be mostly determined by
con-vention, the choice of the overall well-being threshold ϕ seems more arbitrary and less grounded since it works across the dimensions where general understanding is hard to be applied. We take 0.6 as the well-being threshold in all the analysis and conduct a sensitivity analysis of the robustness of the results with respect to the choice of this parameter.
FOR APPROVAL
Table 1 Dimensions, indicators and thresholds
Dimensions Achievement Thresholds Percentage meeting the
Indicators (meet the minimum standard if) minimum standards Economic Per-capita net income equal or above 60 % of median 78.82
(country specific)
Per-capita net wealth equal or above 60 % of median 66.70 (country specific)
Housing Dwelling accessibility less than 16 steps to climb 82.62 up/down to entrance
Chronic disease none of household members have 44.53 more than two chronic diseases
Health ADL none of household members have 86.26
ADL problem
EURO-D none of household members have 66.83
EURO-D caseness
Note: The percentage meeting the minimum standard of a given indicator is a weighted average for the entire sample of households
5 Results
5.1 Life satisfaction and hedonic regression
To set the hedonic weights, we exploit the individual question about life satisfaction in gen-eral. The top panel of Table3shows that about 77 % of the interviewed individuals declared to be satisfied or very satisfied, while 5.4 % declared to be dissatisfied or very dissatisfied. The lower panel provides a first insight on the relation between achievements and life sat-isfaction. For each achievement indicator, we compute the risk ratios for every level of life satisfaction, that is, the ratio of the probability that individuals deprived in that indicator declare a given level of satisfaction, over the same probability for those not deprived. Thus, we see that the percentage of income-poor individuals who declared themselves to be very satisfied with their life is only 3/4 of those whose income is above the income threshold. Viceversa, the percentage of dissatisfied among the income-poor is the double of those with higher income. The differences between being below and above the thresholds of indicators
Table 2 Tetrachoric correlation coefficients among indicatorsah k
Per-capita Per-capita Dwelling Chronic ADL EURO-D
net income net wealth accessibility disease Per-capita net income 1.0000
Per-capita net wealth 0.3565 1.0000
Dwelling accessibility −0.0164 0.2384 1.0000
Chronic disease 0.0253 0.2000 0.0476 1.0000
ADL 0.1155 0.2067 −0.0500 0.5238 1.0000
FOR APPROVAL
Table 3 Distribution of the answers to the life-satisfaction question and relative risk ratios for each life
satisfaction level by indicator
Very Dissatisfied Neither satisfied Satisfied Very
dissatisfied nor dissatisfied satisfied
Percentage of 0.63 4.80 17.48 56.77 20.32
respondents
Relative risk ratios of deprived vs non deprived
Per-capita net income 2.74 2.02 1.36 0.90 0.74
Per-capita net wealth 1.82 1.79 1.47 0.97 0.61
Dwelling accessibility 1.63 1.54 1.60 0.95 0.57
Chronic disease 5.84 2.24 1.29 0.97 0.72
ADL 6.62 2.97 1.72 0.85 0.42
EURO-D 4.40 5.85 1.89 0.85 0.45
Note: Sample of 5545 individuals used to estimate the hedonic weights. The relative risk ratio is the ratio of the fraction of deprived individuals declaring a specific level of satisfaction, over the same fraction computed among the non-deprived population.
are even more striking when focusing on the health indicators, suggesting a prominent role played by the health dimension on the overall life-satisfaction of the individuals.
As explained in the Section4, the Hopit model can be seen as a generalization of the standard ordered probit model which exploits the information provided by the vignette eval-uations to account for heterogeneity in response style. Table 4shows the distribution of respondents’ evaluations of the life satisfaction of the hypothetical individuals described in the vignettes. While about 44 % of respondents rate John (the person in vignette 1) as very dissatisfied or dissatisfied with his life, only 15 % of them think that John is at least sat-isfied. Also, while 13 % of respondents rate Carry (the person in the second vignette) as dissatisfied or very dissatisfied, 55 % of the sample think she is at least satisfied. Although the same vignettes about John and Carry have been administered to all the respondents, their evaluations show considerable variability and suggest the presence of heterogeneity in the way they report life satisfaction. If this is an issue, comparisons of life satisfac-tion self-assessments neglecting this source of heterogeneity might bring about misleading results.
We estimate the hedonic weights considering a full set of observable household and indi-vidual characteristics: country of residence, gender, age, presence of a cohabiting partner,
Table 4 Distribution of the answers to the vignette evaluation
Very Dissatisfied Neither satisfied Satisfied Very
dissatisfied nor dissatisfied satisfied
Vignette 1 (John)
Percentage of respondents 5.78 38.59 40.35 14.32 0.96
Vignette 2 (Carry)
Percentage of respondents 1.30 11.83 30.58 48.65 7.63
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Table 5 Weights derived from different approaches
Equal weights Frequency weights Hedonic weights
Ordered probit Hopit model
Per-capita net income 0.1667 0.1851 0.0569 0.1092
Per-capita net wealth 0.1667 0.1567 0.1167 0.1629
Dwelling accessibility 0.3333 0.1940 0.0986 0.0751
Chronic disease 0.1111 0.1046 0.1314 0.0788
ADL 0.1111 0.2026 0.2626 0.2359
EURO-D 0.1111 0.1570 0.3338 0.3380
children, and grandchildren, employment status, involvement in social activities, education, home ownership, type of the area the accommodation is located in, season at the time of the interview (seeAppendixfor the descriptive statistics).
The regression results (inAppendix) for the ordered probit and Hopit model show that the achievement indicators are strongly correlated with the self-reported life satisfaction and that demographic characteristics play a significant role.11 Life satisfaction exhibits remarkable cross-country heterogeneity, it is higher for women, it is at its minimum among individuals aged between 50 and 55, which is consistent with Blanchflower and Oswald (2008) and de Ree and Alessie (2011). Further, life satisfaction increases with the presence of a cohabiting partner, the involvement in social activities and with being at work or retiree instead of out of work due to reasons other than retirement. As long as the achievement indi-cators are correlated with this set of individual and household characteristics, omitting the latter from the right-hand side of the regression will lead to a biased estimate of the actual relationship between life satisfaction and the achievement indicators (Schokkaert2007).
When we use the Hopit model to control for the possible effect of the heterogeneity in response styles due to differential item functioning (DIF), we can see that this is correlated with country and seasonal dummies, age, the presence of a cohabiting partner, employment status, home-ownership, and the type of area in which the accommodation is located. Some of the achievement indicators, in particular those related to the presence of chronic diseases or depression symptoms, affect the thresholds τij. Overall, our results confirm the evidence provided by Angelini et al. (2012and2014) that there is heterogeneity in the response styles. Therefore, the estimation of the hedonic weights can be biased if such heterogeneity is neglected.
5.2 Comparing alternative weighting schemes
The four sets of weights are presented in Table5. We set the equal weights mimicking the Human Development Index and Multidimensional Poverty Index, that is, the three dimen-sions have the same relevance and the achievement indicators share the same weight within each dimension (UNDP2011). For the frequency weights, we follow Desai and Shah (1988)
11We refrain from interpreting these estimates in terms of causal effects because of the possible endogeneity
of some of the explanatory variables. The estimated coefficients gauge the partial correlation of the variables with the reported life satisfaction.
FOR APPROVAL
Table 6 Dimensional decomposition
Equal weights Frequency weights Hedonic weights
Ordered probit Hopit model
H 0.2380 0.2759 0.3112 0.3165
M 0.1364 0.1496 0.1881 0.1848
Relative contribution of indicators and dimensions to the overall adjusted headcount index M (%)
Per-capita net income 13.10 15.21 2.68 5.70
Per-capita net wealth 20.03 20.26 9.66 13.72
Economic dimension 33.13 35.46 12.34 19.42 Dwelling accessibility 36.03 12.67 4.14 3.11 Housing dimension 36.03 12.67 4.14 3.11 chronic disease 15.32 17.38 18.75 11.35 ADL 5.49 14.20 14.97 13.38 EURO-D 10.02 20.28 49.80 52.75 Health dimension 30.84 51.86 83.52 77.48
Note: The relative contribution of each dimension is the sum of the relative contributions of the corresponding indicators
to set the weight of every achievement indicator as the proportion of the non-deprived households in the sample.12
As compared with the equal weighting scheme, the frequency one reduces the weight of the housing domain from 33.33 % to 19.40 % in favor of the health conditions, whose weight goes from 33.33 % to 46.42 %. The weights attached to the economic conditions remain almost unchanged. As compared with frequency weights, the hedonic approach dou-bles the weight of the EURO-D indicator to about 33 %, and in general it increases the prominence of the health domain. The weights of net income and net wealth are lower in the hedonic weights than in the other two schemes, and they are particularly low for the weights computed with the ordered probit model. With the hedonic weights, the accessibility of the accommodation loses most of its relevance.
Each weighting scheme gives origin to a different well-being score. Setting the poverty threshold ϕ equal to 0.6 produces four headcount ratios that vary between 23.8 % of the equal weights and 31.7 % of the hedonic weights with the vignettes, whereas the corresponding adjusted headcount ratios M range between 13.6 % and 18.8 % (see Table6). Although the level of the adjusted headcount indices is similar across alternative weight-ing structures, the relative contribution of the dimensions is remarkably different. As pointed out in Section2, the relative contribution of each dimension comes from the summation of the relative contributions of all indicators in the dimension. Consider the health dimension: its contribution to the overall level of the adjusted headcount index is 51.9 % for the fre-quency weights and 77.5 % for the hedonic weights taking the heterogeneity in response styles into account (Table6). This variation is driven by the sharp increase in the relative contribution of the EURO-D indicator, which changes from 20.28 % to 52.75 %. As for
12 Frequency weights are standardized in order to sum up to one. Equal weights are standardized by
FOR APPROVAL
Table 7 Adjusted headcount decomposition by age class, by weighting scheme
Age class Population share (%) Subgroup adjusted headcount ratio (Mg)
Equal Frequency Hedonic weights
(θg) weights weights Ordered probit Hopit model
55 or less 17.93 0.1040 0.0888 0.1207 0.1266
56–60 18.64 0.1353 0.1345 0.1709 0.1696
61–65 15.88 0.1269 0.1287 0.1635 0.1589
66–75 28.22 0.1388 0.1412 0.1770 0.1730
76+ 19.34 0.1718 0.2500 0.3034 0.2917
the economic condition, its relative contribution is 35.5 % with frequency weighting and reduces to 12.3 % with hedonic weighting based on the ordered probit model. Most of this reduction is explained by the change in the contribution of the per-capita income indicator that shrinks by about 80 %. This variability magnifies for the housing dimension: it explains more than one third of poverty under equal weighting but only 3 % under the hedonic weighting based on the Hopit model.13
Besides, the differences between subgroups can be affected by the weighting structure too. For instance, if we look at Table7, we find that the households where the oldest member is aged 55 or less experience the lowest level of poverty, whereas those in which the oldest member is aged 76 or more the highest. However, while the adjusted headcount ratio of the youngest households is 40 % lower than the one of oldest households under equal weighting, this reduction is around 60 % for the remaining weighting schemes.
Alternative weighting schemes may deliver remarkably different pictures of poverty dynamics over time (e.g. Bourguignon and Chakravarty2003) as well as different evalua-tions of anti-poverty policies. Consider for instance a hypothetical intervention that solves income deprivation. Table 8 shows that if the intervention were evaluated using equal weights, the policy maker would register 6.16 % of the population exiting the poverty sta-tus and 4.57 % enjoying the benefits of the policy without exiting poverty. In terms of adjusted headcount ratio, starting from an initial level of M = 0.1364 (see Table6), the policy would produce a reduction of M = −0.0383 (−28.1 %), almost completely due to the well-being improvement of those exiting the poverty status (M1/M = 80.2 %). The same policy evaluated with the hedonic weights computed with the ordered probit would account for only 1.01 % of the population exiting poverty, a very limited reduc-tion of M (M = −0.0086, a mere − 4.6 %), only half of it originated by households escaping poverty (M1/M = 49.1 %). That such a policy would be judged more effec-tive using equal weights rather than hedonic weights may seem obvious, given that in the first case the weight for income achievement is 0.1667 while in the latter is 0.0569. But this is not always the case. Assume the policy maker were able to eradicate ADL deprivation, whose weight is 0.2026 with frequency weights and 0.2626 for hedonic weights
13We carried out a sensitivity analysis by setting an alternative poverty threshold ϕ = 0.47, that is the 60
% of the median of the well-being score computed with the equal weights. Our results are confirmed. In order to check whether the number of indicators per dimension drives the decomposition analysis, we also estimated two alternative sets of hedonic weights by replacing the indicators in the ordered probit and Hopit models with their averages by dimension. By doing this, we estimate one parameter for each dimension, the indicators within a given dimension equally split the dimensional weight and are finally standardized. Our results are again confirmed.
FOR APPROVAL
Table 8 Effects of interventions under different weighting schemes
Indicator targeted Weighting Relative group Group-specific adjusted Overall adjusted headcount by the policy schemes size (%) headcount index changes index change
nout/n nst ay/n ΔMout ΔMst ay ΔM ΔM1
Per capita net 1 6.16 4.57 −0.4988 −0.1667 −0.0383 −0.0307
income 2 5.61 6.68 −0.4732 −0.1851 −0.0389 −0.0265 3 1.01 7.87 −0.4131 −0.0569 −0.0086 −0.0042 4 1.86 7.79 −0.4390 −0.1092 −0.0167 −0.0082 ADL 1 2.87 3.87 −0.4960 −0.1111 −0.0186 −0.0142 2 4.20 6.29 −0.4774 −0.2026 −0.0328 −0.0200 3 2.54 8.18 −0.5506 −0.2626 −0.0355 −0.0140 4 2.08 8.40 −0.5321 −0.2359 −0.0309 −0.0111
Note: 1- equal weights, 2 - frequency weights; 3 - hedonic weights based on ordered probit; 4 - hedonic weights based on the Hopit model
derived from the ordered probit model. Such intervention turns out to be more effective if assessed under frequency weighting rather than the hedonic weighting scheme considered since the relative variation in the M amounts to M/M= −0.328/0.1496 = −21.9 % and M/M= −0.0355/0.1881 = −18.9 % respectively.
If we look at the effects of the interventions under the hedonic weights based on the Hopit model, we find that they are extremely close to their analogues under the alternative set of hedonic weights. In particular, the percentages of households exiting the poverty status or enjoying the benefits of the policy without exiting poverty and the variation in the adjusted headcount ratio explained by well-being improvement of the households exiting the poverty status are virtually unaffected. We interpret these results as evidence in favor of the stability of the poverty assessment with hedonic weights to the relaxation of the assumption of invariance of reporting styles in the population.
Finally, Table9helps to understand the origin of the differences between poverty mea-surements by decomposing the variation of the adjusted headcount ratios observed in Table6. Abandoning the equal weights for the frequency weights, 4.98 % of the population exits the poverty status, while 8.77 % enters it. Despite the fact that the correlation between the two well-being scores is 94.8 %, only 79.1 % of the poor under equal weights are clas-sified as such also with the frequency weights. The overall change in the headcount ratio is M= 0.0132 (+9.7 % with respect to the starting level of M = 0.1362), the variation due to the change in the pool of households in poverty is M1 = 0.0162, and, consequently, the variation in the poverty assessment of the households identified as poor under both weight-ing schemes is M2 = 0.0132 − 0.0162 = −0.003. The M1component predominates over M2. This decomposition shows that the information provided by the achievements of the set of households originally classified as poor is insufficient to predict the variations in the poverty assessments due to the changes in the weighting schemes. Most of the variation in the adjusted headcount ratio is explained by the outcomes of the households changing their poverty status from one weighting scheme to the other.
Although going from equal weights to the hedonic weights computed with the ordered probit, implies a wider reshuffle of the set of poor households, the contribution of this component to the overall change of the adjusted headcount ratio is lower (M1/M =
FOR APPROVAL
Table 9 Effects of changes of weighting scheme on the adjusted headcount ratio M
Weighting Relative group Group-specific adjusted Overall adjusted
schemes size (%) headcount ratio changes headcount ratio change
From w To w nout/n nin/n nst ay/n ΔMout ΔMin ΔMst ay ΔM ΔM1
1 2 4.98 8.77 18.82 −0.4636 0.4480 −0.0162 0.0132 0.0162
3 9.19 16.51 14.61 −0.5126 0.5456 0.0592 0.0516 0.0430
3 4 0.25 0.77 30.88 −0.4926 0.4472 −0.0180 −0.0033 0.0022
Note: 1- equal weights, 2 - frequency weights; 3 - hedonic weights based on ordered probit; 4 - hedonic weights based on the Hopit model
0.043/0.0516 = 83 %). The same table shows also that the two hedonic weight vectors deliver two poverty measurements that are barely distinguishable from each other: the varia-tion in the adjusted headcount ratio is a mere 0.1 %. Furthermore, 99.2 % of the households classified as poor with one set of weights are poor also according to the other weighting scheme. This finding, together with the 98.5 % correlation between the two scores, clearly shows that, in our sample, the poverty measurement based on the hedonic weights is not significantly affected by the presence of reporting styles heterogeneity in life satisfaction self-assessments.
6 Conclusions
Using multidimensional poverty measures instead of simple monetary poverty indicators is now a standard practice. The increase in the number and heterogeneity of the dimensions makes the weighting scheme a key ingredient of the poverty assessment. In this paper we carry out a multidimensional poverty assessment framed in the approach proposed by Alkire and Foster (2011a) to assess empirically to what extent the outcomes of a multidimensional poverty analysis depends on the weighting scheme adopted and whether the use of hedonic weights derived from self-assessed life satisfaction questions is robust to the presence of heterogeneity in response styles.
We draw data from the second wave of SHARE, a multi-country survey of the Euro-peans aged 50 or over, consider three dimensions (economic, housing and health) and compute the headcount and the adjusted headcount ratios using equal, frequency and hedo-nic weighting schemes. Two sets of hedohedo-nic weights are estimated, one by means of an ordered probit regression having respondents’ life satisfaction self-assessments as depen-dent variable, the other using a Hopit model, a model which takes into account the variability of response styles across individuals by means of an anchoring vignette methodology (King et al.2004).
Our results show that changes in the weighting scheme produces substantial differences in poverty assessment, both in terms of headcount and adjusted headcount ratios. Decom-posing the variation of the adjusted headcount ratio, we see that the pools of households entering or exiting poverty when varying the weighting scheme can explain most of the differences in the measurement of poverty. Moreover, the contribution of each dimension to the overall poverty level changes widely across alternative weighting schemes, the same holds true for the contribution of different subgroups of households and for the evaluation of hypothetical policy interventions.
FOR APPROVAL
Although our empirical exercise confirms that the heterogeneity in response styles is an important issue in modeling life satisfaction self-assessments, it does not highlight signifi-cantly differences in neither the level nor the decomposition of the poverty index based on the hedonic weights. Overall, our results based on hedonic weights proved to be robust to the relaxation of the assumption that the reporting styles adopted by individuals in assessing life satisfaction are invariant in the population.Our empirical results relate to a sample of Europeans aged 50 or over, and they are influ-enced by the framework adopted and by the achievements considered. Nevertheless, they clearly warn us that the choice of the weighting schemes is not innocuous for the outcomes of a multidimensional poverty analysis. Comparisons of poverty across groups and pol-icy evaluations should then take into account this issue in order to provide meaningful and reliable conclusions.
Acknowledgments This paper uses data from SHARE wave 4 release 1.1.1, as of March 28th2013 or
SHARE wave 1 and 2 release 2.5.0, as of May 24th2011 or SHARELIFE release 1, as of November 24th
2010. The SHARE data collection has been primarily funded by the European Commission through the 5th Framework Programme (project QLK6-CT-2001-00360 in the thematic programme Quality of Life), through the 6th Framework Programme (projects SHARE-I3, RII-CT-2006-062193, COMPARE, CIT5-CT-2005-028857, and SHARELIFE, CIT4-CT-2006-028812) and through the 7th Framework Programme (SHARE-PREP, N◦211909, SHARE-LEAP, N◦227822 and SHARE M4, N◦261982). Additional fund-ing from the U.S. National Institute on Agfund-ing (U01 AG09740-13S2, P01 AG005842, P01 AG08291, P30 AG12815, R21 AG025169, Y1-AG-4553-01, IAG BSR06-11 and OGHA 04-064) and the German Min-istry of Education and Research as well as from various national sources is gratefully acknowledged (see www.share-project.org for a full list of funding institutions). We are grateful to the Editor and two anonymous referees for helpful comments and suggestions. We also thank the participants at the Italian SHARE Users’ Conference (2012), 12th Journ´ees Louis-Andr´e G´erard-Varet Conference in Public Economics (2013), SIS 2013 Statistical Conference, ASSET Annual Meeting (2013), International SHARE User Conference (2013), NETSPAR International Pension Workshop (2014), ESPE Annual Conference (2014) and at seminars at the University of Groningen and CEMFI.
Appendix: ML estimates of ordered probit and Hopit models, and sample mean of covariates
Table 10 ML estimates of ordered probit and Hopit models, and sample mean of covariates
Ordered Hopit model probit model
main /cutoff1 /cutoff2 /cutoff3 /cutoff4 Sample
equation mean
per-capita net income 0.0876∗ 0.1662∗∗∗ 0.0358 0.0295 −0.0043 −0.0111 0.8399 per-capita net wealth 0.1797∗∗∗ 0.2480∗∗∗ 0.0963 −0.0505 0.0604 −0.0171 0.7078 dwelling accessibility 0.1518∗∗∗ 0.1143∗ −0.1555∗ 0.0426 −0.0033 0.0775∗∗ 0.8465 chronic disease 0.2022∗∗∗ 0.1200∗∗∗−0.1327∗∗ 0.0467 −0.0123 −0.0125 0.4298 ADL 0.4043∗∗∗ 0.3591∗∗∗−0.1222 0.0262 0.0384 0.0111 0.8871 EURO-D 0.5138∗∗∗ 0.5145∗∗∗−0.1899∗∗∗ 0.0403 0.0702∗∗ 0.0806∗∗∗ 0.6967 SE 0.3422∗∗∗ 0.3828∗∗∗ 0.5189∗∗∗ −0.0508 −0.1528∗∗ −0.2432∗∗∗ 0.0772 DK 0.5840∗∗∗ 0.0268 −0.2729 −0.0260 −0.1010 −0.1474∗∗∗ 0.1717 NL 0.2203∗∗∗ 0.5862∗∗∗ 0.6714∗∗∗ −0.2989∗∗∗ 0.0175 0.0311 0.0833
FOR APPROVAL
Table 10 (continued)
Ordered Hopit model probit model
main /cutoff1 /cutoff2 /cutoff3 /cutoff4 Sample
equation mean BE 0.0184 −0.0292 0.5334∗∗∗ −0.0797 −0.2115∗∗∗ −0.2839∗∗∗ 0.0931 FR −0.1265 0.2492∗ 0.7092∗∗∗ −0.1762 0.0335 −0.0560 0.0637 GR −0.5224∗∗∗ −0.5964∗∗∗ 0.5848∗∗∗ −0.1854 −0.0299 −0.6128∗∗∗ 0.0895 IT −0.3165∗∗∗ −0.0312 0.7414∗∗∗ −0.1196 −0.2477∗∗∗ 0.0136 0.1068 ES 0.0061 0.0636 0.5812∗∗∗ −0.0416 −0.4044∗∗∗ −0.0927 0.0828 CZ −0.2729∗∗∗ −0.5580∗∗∗−0.0003 −0.1265 −0.0038 −0.0682 0.1473 male −0.1078∗∗∗ −0.0807∗ 0.0152 0.0034 0.0050 0.0107 0.4449 aged 55 or less −0.2000∗∗∗ −0.4066∗∗∗−0.1798 0.0188 −0.0290 −0.0366 0.2341 aged 56− 60 −0.0541 −0.1977∗∗ −0.0669 −0.0300 −0.0042 −0.0422 0.2076 aged 61− 65 −0.0098 −0.0918 −0.2059∗ 0.0928 −0.0147 −0.0177 0.1729 aged 66− 75 0.0011 0.0419 0.1722∗ −0.0904 0.0254 −0.0433 0.2530
living with cohabiting 0.4119∗∗∗ 0.4279∗∗∗−0.0182 0.0111 −0.0242 0.0700∗∗ 0.7803 have children 0.0051 −0.0167 −0.0778 0.0934 −0.0384 −0.0491 0.9039 have grand children 0.0386 0.0737 −0.0023 −0.0018 0.0256 0.0178 0.6388 retired from work 0.2053∗∗∗ 0.2827∗∗∗ −0.0393 0.0450 0.0257 0.0527 0.4956 employed or 0.2458∗∗∗ 0.4288∗∗∗ −0.0913 0.0889 0.0581 0.1136∗∗∗ 0.3203 self-employed not involved in −0.2266∗∗∗ −0.2536∗∗∗ 0.0989 −0.0808∗ 0.0443 −0.0643∗∗∗ 0.4923 social activity low education −0.0233 −0.0491 −0.1170 0.0525 −0.0016 0.0183 0.4855 middle education −0.0059 −0.0110 −0.0245 −0.0232 0.0095 0.0473 0.2819 house owner −0.0388 −0.0558 −0.0772 0.0194 −0.0261 0.0668∗∗ 0.7482 residing in city 0.0643 0.0739 0.0640 −0.0205 −0.0650∗ 0.0476 0.3234 residing in town 0.1142∗∗∗ 0.0600 −0.0401 0.0171 −0.0733∗∗ 0.0516∗ 0.4227 interviewed in winter −0.0045 −0.0991 0.1904∗ −0.1983 0.0284 0.0189 0.4074 interviewed in spring 0.0624 0.028 0.2265∗ −0.1574∗∗ 0.0145 −0.0075 0.3627 interviewed in summer−0.0202 −0.1626 0.1554 −0.2489∗ 0.0787 0.0346 0.0294 /cutoff1 −1.4208 – – – – – /cutoff2 −0.3970 – – – – – /cutoff3 0.6308 – – – – – /cutoff4 2.4940 – – – – – vignettes question 1 – −0.4821∗∗∗ – – – – vignettes question 2 – 0.6794∗∗∗ – – – – Constant – – −2.0703∗∗∗ 0.4395∗∗ 0.1647 0.4631∗∗∗ McFadden Pseudo R2 0.1194 0.0711
